Stabilization of Nonlinear Vertical Diffusion Schemes in the Context of NWP Models

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Abstract
The stability of the nonlinear vertical diffusion equation such as commonly used for parameterizing the turbulence in NWP models is examined. As a starting point, this paper adopts the idea of Girard and Delage and shows how their results can be modified when the problem is examined in a less restrictive framework, typical of practical NWP applications. In Girard and Delage’s work, an optimal compromise between stability and accuracy was proposed to eliminate the “fibrillations” resulting from the instability, by applying a time decentering in the diffusion operator for the points likely to be unstable according to a local linear analysis of the stability. This key idea is pursued here, but two important changes are examined: (i) an exact method for the relaxation of the identity between thermal and dynamical exchange coefficients, and (ii) the introduction of a modification to the Richardson number for simulating the destabilization of the top of the PBL in shallow convection conditions. Compare... Abstract The stability of the nonlinear vertical diffusion equation such as commonly used for parameterizing the turbulence in NWP models is examined. As a starting point, this paper adopts the idea of Girard and Delage and shows how their results can be modified when the problem is examined in a less restrictive framework, typical of practical NWP applications. In Girard and Delage’s work, an optimal compromise between stability and accuracy was proposed to eliminate the “fibrillations” resulting from the instability, by applying a time decentering in the diffusion operator for the points likely to be unstable according to a local linear analysis of the stability. This key idea is pursued here, but two important changes are examined: (i) an exact method for the relaxation of the identity between thermal and dynamical exchange coefficients, and (ii) the introduction of a modification to the Richardson number for simulating the destabilization of the top of the PBL in shallow convection conditions. Compare...

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